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1.
Raphaële Supper 《Positivity》2005,9(4):645-665
For functions u subharmonic in the unit ball BN of
, this paper compares the growth of the repartition function of their Riesz measure μ with the growth of u near the boundary
of BN. Cases under study are:
and
, with A, B, γ positive constants and
if N=2 or
if N≥ 3. This paper contains several integral results, as for instance: when ∫BN u+(x)[-ω′(|x|2)]dx < +∞ for some positive decreasing C1 function ω, it is proved that
. 相似文献
2.
Mouez Dimassi 《Annales Henri Poincare》2006,7(3):513-525
In the large-coupling constant limit we obtain an asymptotic expansion in powers of
of the derivative of the spectral shift function corresponding to
. Here the potential W(x) is positive and
near infinity for some δ> n and ω0 ∈C∞ (Sn-1).
submitted 18/05/05, accepted 19/10/05 相似文献
3.
Let X1, X2,... be, i.i.d. random variables, and put
. We find necessary and sufficient moment conditions for
, where δ≥ 0 and q>0, and
with an>0 and bn is either
or
The series f(x) we deal with are classical series studied by Hsu and Robbins, Erdős, Spitzer, Baum and Katz, Davis, Lai, Gut, etc 相似文献
4.
We consider quadratic forms of the type
where Xj are i.i.d. random variables with common distribution F and finite fourth moment,
denotes a symmetric matrix with eigenvalues λ1, ..., λN ordered to be non-increasing in absolute value. We prove explicit bounds in terms of sums of 4th powers of entries of the
matrix A and the size of the eigenvalue λ13 for the approximation of the distribution of Q(F,A) by the distribution of Q (φ, A) where φ is standard Gaussian distribution. In typical cases this error is of optimal order
Supported by the DFG-Forschergruppe FOR 399/1-1 at Bielefeld. Partially supported by INTAS N 03-51-5018.
Partially supported by RFBR and RFBR–DFG, grants NN 02-01-00233, 04-01-04000 相似文献
5.
Let X, Y be Banach spaces. We say that a set
is uniformly p–summing if the series
is uniformly convergent for
whenever (xn) belongs to
. We consider uniformly summing sets of operators defined on a
-space and prove, in case X does not contain a copy of c0, that
is uniformly summing iff
is, where T (φ x) = (T#φ) x for all
and x∈X. We also characterize the sets
with the property that
is uniformly summing viewed in
.
Received: 1 July 2005 相似文献
6.
We determine conditions under which a subordinated random walk of the form
tends to infinity almost surely (a.s), or
tends to infinity a.s., where {N(n)} is a (not necessarily integer valued) renewal process,
denotes the integer part of N(n), and Sn is a random walk independent of {N(n)}. Thus we obtain versions of the Alternatives, for drift to infinity, or for divergence to infinity in the strong law, for
. A complication is that
is not, in general, itself, a random walk. We can apply the results, for example, to the case when N(n)= n, > 0, giving conditions for lim
, a.s., and lim sup
, a.s., etc. For some but not all of our results, N(1) is assumed to have finite expectation. Examples show that this is necessary for the kind of behaviour we consider. The results are also shown to hold in the same degree of generality for subordinated Lévy processes. 相似文献
7.
Let E be a non empty set, let P : = E × E,
:= {x × E|x ∈ E},
:= {E × x|x ∈ E}, and
:= {C ∈ 2
P
|∀X ∈
: |C ∩ X| = 1} and let
. Then the quadruple
resp.
is called chain structure resp. maximal chain structure. We consider the maximal chain structure
as an envelope of the chain structure
. Particular chain structures are webs, 2-structures, (coordinatized) affine planes, hyperbola structures or Minkowski planes.
Here we study in detail the groups of automorphisms
,
,
,
related to a maximal chain structure
. The set
of all chains can be turned in a group
such that the subgroup
of
generated by
the left-, by
the right-translations and by ι the inverse map of
is isomorphic to
(cf. (2.14)). 相似文献
8.
A 1-factorization (or parallelism) of the complete graph with loops
is called polar if each 1-factor (parallel class) contains exactly one loop and for any three distinct vertices x1, x2, x3, if {x1} and {x2, x3} belong to a 1-factor then the same holds for any permutation of the set {1, 2, 3}. To a polar graph
there corresponds a polar involution set
, an idempotent totally symmetric quasigroup (P, *), a commutative, weak inverse property loop (P, + ) of exponent 3 and a Steiner triple system
.
We have:
satisfies the trapezium axiom
is self-distributive ⇔ (P, + ) is a Moufang loop
is an affine triple system; and:
satisfies the quadrangle axiom
is a group
is an affine space. 相似文献
9.
Venkat Anantharam 《Queueing Systems》2006,52(3):185-188
Given n−1 points
on the real line and a set of n rods of strictly positive lengths
, we get to choose an n-th point xn anywhere on the real line and to assign the rods to the points according to an arbitrary permutation π. The rod
is thought of as the workload brought in by a customer arriving at time xk into a first in -first out queue which starts empty at − ∞. If any xi equals xj for i < j, service is provided to the rod assigned to xi before the rod assigned to xj.
Let
denote the set of departure times of the customers (rods). Let
denote the number of choices for the location of xn for which
. Rybko and Shlosman proved that
for Lebesgue almost all
.
Let
denote the departure point of the rod λk. Let Nπ, k(y) denote the number of choices for the location of xn for which
and let
. In this paper we prove that for every
and every k we have
for all but finitely many y. This implies (and strengthens) the rod placement theorem of Rybko and Shlosman.
AMS Subject Classifications: 60G55, 05A05, 60C05, 60K25
Research supported by ONR MURI N00014-1-0637, NSF ECS-0123512, Marvell Semiconductor, and the University of California MICRO
program. 相似文献
10.
Self-dual 2–forms on
play a fundamental role in gauge theory. For generalized Seiberg-Witten theory (and for some other purposes in mathematical
physics) a notion of self-duality of 2–forms on
is needed. There are several definitions, but the one given by [Bilge, Dereli, Ko?ak ; JMP 38(9), 1997] is intimately related
with Clifford algebras. They defined a 2–form
to be self-dual if the anti-symmetric matrix Ω = (ωij) satisfies Ω2 = λ I for a scalar λ and proved that the space
of such forms is non-linear with dimension n2 − n + 1, but contains maximal linear subspaces with dimension the Radon-Hurwitz number of (2n). It is important to have an algorithm for construction of such maximal linear subspaces and we give an explicit one with
the help of representations of Clifford algebras on
whereby we show that the representations given by the standart recursion formulas are anti-symmetric. 相似文献
11.
12.
The asymptotic expansions are studied for the vorticity
to 2D incompressible Euler equations with-initial vorticity
, where ϕ0(x) satisfies |d ϕ0(x)|≠0 on the support of
and
is sufficiently smooth and with compact support in ℝ2 (resp. ℝ2×T) The limit,v(t,x), of the corresponding velocity fields {v
ɛ(t,x)} is obtained, which is the unique solution of (E) with initial vorticity ω0(x). Moreover,
(ℤ2)) for all 1≽p∞, where
and ϕ(t,x) satisfy some modulation equation and eikonal equation, respectively. 相似文献
13.
Violeta Petkova 《Archiv der Mathematik》2005,84(4):311-324
Let
be a weighted space with weight . In this paper we show that for every Wiener-Hopf operator T on
and for every a I, there exists a function
such that
for all
Here (g)a denotes the function x g(x)eax for
and
where R+ is the spectral radius of the shift S : f(x) f(x–1) on
while
is the spectral radius of the backward shift S–1 : f(x) (P+f)(x+1) on
Moreover, there exists a constant C, depending on , such that
for every a I. If R– < R+, we prove that there exists a bounded holomorphic function v on
such that for
the function va is the restriction of v on the line
Received: 18 May 2004 相似文献
14.
Asymptotic Normality for Non-linear Functionals of Non-causal Linear Processes with Summable Weights
Let
be a non-causal linear process with weights ajs satisfying certain summability conditions, and the iid sequence of innovation {i} having zero mean and finite second moment. For a large class of non-linear functional K which includes indicator functions and polynomials, the present paper develops the
central limit theorem for the partial sums
相似文献
15.
Singular Integrals and Commutators in Generalized Morrey Spaces 总被引:1,自引:0,他引:1
Lubomiea Softova 《数学学报(英文版)》2006,22(3):757-766
16.
Let T be an M-hyponormal operator acting on infinite dimensional separable Hilbert space and let
be the Riesz idempotent for λ0, where D is a closed disk of center λ0 which contains no other points of σ (T). In this note we show that E is self-adjoint and
As an application, if T is an algebraically M-hyponormal operator then we prove : (i) Weyl’s theorem holds for f(T) for every
(ii) a-Browder’s theorem holds for f(S) for every
and f ∈ H(σ(S)); (iii) the the spectral mapping theorem holds for the Weyl spectrum of T and for the essential approximate point spectrum of T. 相似文献
17.
Carlos E. Durán Luis E. Mata-Lorenzo Lázaro Recht 《Integral Equations and Operator Theory》2005,53(1):33-50
This article focuses on the study of the metric geometry of homogeneous spaces
(the unitary group of a C*-algebra
modulo the unitary group of a C*-subalgebra
) where the invariant Finsler metric in
is induced by the quotient norm of
Under the assumption that
is of compact type, i.e. when the unitary group is relatively compact in the strong operator topology, this work presents local and global versions of Hopf-Rinow-like theorems: given points
there exists a minimal uniparametric group curve joining ρ0 and ρ1. 相似文献
18.
Summary.
Let
be a field of real or complex numbers and
denote the set of nonzero elements of
.
Let
be an abelian group. In this paper, we solve the functional equation
f
1
(x +
y) +
f
2
(x -
y) =
f
3
(x) +
f
4
(y) +
g(xy)
by modifying the domain of the unknown functions
f
3,
f
4, and
g from
to
and using a method different from [3]. Using this result,
we determine all functions
f
defined on
and taking values on
such that the difference
f(x + y) + f
(x -
y) - 2
f(x) - 2
f(y)
depends only on the product
xy for all
x and
y in
相似文献
19.
Xiong Ping DAI 《数学学报(英文版)》2006,22(1):301-310
Let (X, G(X), m) be a probability space with a-algebra G(X) and probability measure m. The set V in G is called P-admissible, provided that for any positive integer n and positive-measure set Vn∈ contained in V, there exists a Zn∈G such that Zn belong to Vn and 0 〈 m(Zn) 〈 1/n. Let T be an ergodic automorphism of (X, G) preserving m, and A belong to the space of linear measurable symplectic cocycles 相似文献
20.
Hendrik Vogt 《Annales Henri Poincare》2009,10(2):395-414
We study Schr?dinger operators on formally given by , where μ is a positive, compactly supported measure from the Kato class. Under the assumption that a certain condition on
the μ-volume of balls is satisfied and that Hμ has at least two eigenvalues below the essential spectrum , we derive a lower bound on the first spectral gap of Hμ. The assumption on the μ-volume of balls is in particular satisfied if μ is of the form , where M is a compact (n-1)-dimensional Lipschitz submanifold of , σM the surface measure on M, and .
Submitted: May 8, 2008.; Accepted: February 20, 2009. 相似文献